Butler is an all-star caliber player that can play at both ends and happens to play the Spurs' biggest position of need. He isn't on Kawhi's level but he's as close as they could realistically get to replacing him. He's also young enough to where the Spurs could wait out the Dubs for another two years while developing the young players they'd keep (one of Murray/Walker, White, Metu). Heck, it also puts the Spurs another 3&D player away from being a challenge to the Dubs.
Not sure I'd want to pay Butler max money next offseason but from a basketball standpoint he makes perfect sense if the Spurs don't have to sell the farm for him.